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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 342 · 40 sums
TalentJR

The trick (Ekadhikena Purvena): 2, 5, 10: the last digit (even; 0 or 5; 0). 3 and 9: add the digits. 4: the last two digits. 8: the last three digits. 6: even and passes the rule for 3. 11: from the right, add the 1st, 3rd, 5th… digits and the 2nd, 4th… digits; the difference must be 0 or a multiple of 11. Any prime p: multiply p by 1, 3, 7 or 9 so it ends in 9; one more than the digits before the 9 is the osculator (7 → 5, 13 → 4, 17 → 12, 19 → 2, 23 → 7, 29 → 3). Take the last digit × the osculator and add it to the rest; repeat until the number is small and check the times table. Composite numbers: split into two factors that share no factor and pass BOTH rules — 6 = 2 × 3, 12 = 3 × 4, 15 = 3 × 5, 18 = 2 × 9, 20 = 4 × 5, 24 = 3 × 8, 30 = 3 × 10.

NameDateTime takenScore ___ / 40
  1. 1.Is 2064 divisible by 12?
  2. 2.Is 120692 divisible by 20?
  3. 3.Is 42810 divisible by 30?
  4. 4.Is 21150 divisible by 10?
  5. 5.Is 12257 divisible by 2?
  6. 6.Is 47268 divisible by 9?
  7. 7.Is 58431 divisible by 12?
  8. 8.Is 12104 divisible by 8?
  9. 9.Is 7008 divisible by 4?
  10. 10.Is 32820 divisible by 5?
  11. 11.Is 84871 divisible by 17?
  12. 12.Is 44836 divisible by 11?
  13. 13.Is 29527 divisible by 29?
  14. 14.Is 1666 divisible by 7?
  15. 15.Is 141536 divisible by 23?
  16. 16.Is 7266 divisible by 6?
  17. 17.Is 37409 divisible by 8?
  18. 18.Is 36569 divisible by 8?
  19. 19.Is 92112 divisible by 30?
  20. 20.Is 59559 divisible by 29?
  21. 21.Is 51241 divisible by 10?
  22. 22.Is 28449 divisible by 9?
  23. 23.Is 6174 divisible by 3?
  24. 24.Is 4016 divisible by 6?
  25. 25.Is 45753 divisible by 17?
  26. 26.Is 17710 divisible by 5?
  27. 27.Is 21990 divisible by 6?
  28. 28.Is 8464 divisible by 10?
  29. 29.Is 19310 divisible by 4?
  30. 30.Is 31136 divisible by 5?
  31. 31.Is 89243 divisible by 19?
  32. 32.Is 60610 divisible by 17?
  33. 33.Is 28992 divisible by 6?
  34. 34.Is 18252 divisible by 18?
  35. 35.Is 40962 divisible by 6?
  36. 36.Is 36741 divisible by 12?
  37. 37.Is 27307 divisible by 18?
  38. 38.Is 159467 divisible by 30?
  39. 39.Is 16416 divisible by 18?
  40. 40.Is 189602 divisible by 29?

Answer key

  1. yes
  2. no
  3. yes
  4. yes
  5. no
  6. yes
  7. no
  8. yes
  9. yes
  10. yes
  11. no
  12. yes
  13. no
  14. yes
  15. no
  16. yes
  17. no
  18. no
  19. no
  20. no
  21. no
  22. yes
  23. yes
  24. no
  25. no
  26. yes
  27. yes
  28. no
  29. no
  30. no
  31. yes
  32. no
  33. yes
  34. yes
  35. yes
  36. no
  37. no
  38. no
  39. yes
  40. yes

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